(2+i^6)-(1-i^2)

Jasonbradley

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Jun 16, 2024

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Simplifying Complex Expressions: (2 + i^6) - (1 - i^2)

This article will guide you through the process of simplifying the complex expression: (2 + i^6) - (1 - i^2)

Understanding Complex Numbers

Complex numbers are numbers that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, defined as the square root of -1 (i.e., i² = -1).

Simplifying the Expression

1. Simplify the powers of i:

   • i^6: Remember that i² = -1. We can rewrite i^6 as (i²)³ = (-1)³ = -1.
   • i^2: As mentioned earlier, i² = -1.

2. Substitute the simplified powers:

   • Our expression now becomes: (2 + (-1)) - (1 - (-1))

3. Simplify the expression:

   • (2 - 1) - (1 + 1) = 1 - 2 = -1

Final Result

Therefore, the simplified form of the expression (2 + i^6) - (1 - i^2) is -1.